Math Problem Statement

The distance between two cities on a map is 3.5 centimeters. The map uses a scale in which 1 centimeter represents 20 kilometers.

What is the actual distance between these two cities in kilometers?

A.55 km

B.60 km

C.65 km

D.70 km

Solution

To find the actual distance between the two cities, we can use the scale provided by the map.

  • The map shows a scale where 1 centimeter represents 20 kilometers.
  • The distance on the map is 3.5 centimeters.

To calculate the actual distance, multiply the map distance by the scale:

Actual distance=3.5cm×20km/cm=70km\text{Actual distance} = 3.5 \, \text{cm} \times 20 \, \text{km/cm} = 70 \, \text{km}

So, the actual distance between the two cities is 70 kilometers.

The correct answer is D. 70 km.

Would you like further details on this, or do you have any questions?

Here are 5 related questions:

  1. How would the actual distance change if the map distance was doubled?
  2. What would the scale be if 1 centimeter represented 10 kilometers instead?
  3. If the actual distance between two cities was 140 km, how far apart would they be on the map using the same scale?
  4. What is the map distance if the actual distance between two cities is 210 kilometers, using the given scale?
  5. How would the scale change if 3.5 cm represented only 35 kilometers?

Tip: Always remember to multiply or divide by the scale ratio to switch between map distances and actual distances.

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Math Problem Analysis

Mathematical Concepts

Proportions
Scale Factors

Formulas

Actual distance = Map distance × Scale ratio

Theorems

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Suitable Grade Level

Grades 5-7